A necessary trait of all living organisms is their adaptability. They are governed by processes that adapt to external/non-genetic perturbations (homeostasis) and are robust to internal mutational/genetic changes (referred to here as robustness, for simplicity). Mathematically, a priori, these two concepts are unrelated: Natural selection is determined by the survival and reproductive capabilities, in particular homeostasis, of an individuals phenotype. Homeostasis is a dynamic property. On the other hand, germline mutations change the genotype of progeny without affecting the fitness of the parent. Robustness is, however, necessary for an individuals phenotype to be transmitted to progeny, and is a static property. In fact, many biological networks that protect the organism against changes in the environment are also able to prevent phenotypic changes due to genetic mutation. The aim of this study is to investigate the effect of network topologies on their capacity for adaptation and to arrive at a quantitative description of the relationship between homeostasis and robustness. We analyzed all possible topologies of three-node enzymatic networks using a quantitative measure of the degree of robustness to both input and parameter perturbations. After selecting for adaptable networks using the Pearson correlation, we found a strong statistical correlation between adaptable homeostasis and robustness. We investigated the topological motifs that are necessary and/or sufficient to achieve adaptability, homeostasis, and/or robustness. This work is an essential stepping stone towards a quantitative and predictive understanding of the interplay between homeostasis and robustness in natural selection.